This invention relates to interferometric apparatus comprising a rotary scanner of the optical path difference between two optical paths, such as the two arms of an interferometer of the Michelson type, in particular a Michelson interferometer forming part of a Fourier Transform Spectrophotometer, the rotary scanner being such as to enable the beam outputted therefrom to remain substantially fixed in space for any angle of rotation within predetermined scanning limits.
It is believed that, although the phrase "optical path difference" and the related phrases "optical path length" and "geometrical path length" presently to be encountered are well understood in the interferometric art, it would be of assistance to the reader in appreciating their significance in the present context if they were distinguished from the outset.
We will distinguish first the phrases "geometric path length" and "optical path length", in which the path referred to is that followed by light rays between two points spaced along their travel or, more specifically, two spaced optical elements. The "geometrical path length" is simply the length, in any convenient units of linear measure, of the path through air, or any other medium, from one to other of said points. The "optical path length", on the other hand, takes into account the retardation effect on light waves of any intervening medium other than air. By definition, it is the product of the geometrical path length and the refractive index of the medium. The refractive index (usually denoted by the letter n) is in fact a measure of the retardation. If a light wave takes a time t to travel between two spaced points in air, it will take a time t.times.n to travel between the same two points when a medium of index n greater than 1 is substituted. If n=2, for example, the travel time is doubled.
It will be appreciated, therefore, that two light waves initially travelling in phase coincidence along two separate paths of the same geometrical path length (if no media other than air are included in the paths) or optical path length (if media other than air are present) are thrown out of step if one is retarded with respect to the other by increasing the geometrical path length or the optical path length, as the case may be, of one path with respect to the other.
A system of mirrors can clearly be used to change the geometrical path length simply by increasing or decreasing the distance travelled in air by the light rays. It follows that even where refractive elements are present the system will still alter the geometrical length of that portion of the overall path that passes through air and, therefore, it will alter the optical path length, in so far as the latter is derived from the former in the manner hereinbefore referred to.
Two optical paths may have the same geometrical path length and yet one path will cause greater retardation than the other if its optical path length is greater. On the other hand, equality of optical path lengths is always associated with equal retardations. This means that the phrase "optical path length" has greater generality and may conveniently be used in a context where refractive elements may or may not be involved.
As to the phrase "optical path difference", it simply relates to the difference in optical path length between two paths that may include media other than air. The phrase "geometrical path difference" is not often used, but after what has been said in the preceding paragraph, its meaning should be clear.
In the present context, the phrases "optical path length" and "optical path difference" (hereinafter frequently referred to and conveniently denoted by the initials O.P.D.) are intended to be associated with situations where the presence of media other than air is not to be excluded but not necessarily included.
In a basic Michelson-type interferometer, the radiation flux emanating from a source of monochromatic light, either in the visible or the invisible regions of the electromagnetic spectrum, impinges on a beam splitter after passing through a collimator. The beam splitter is oriented at an angle of 45 degrees to the direction of the incoming collimated beam so that a portion (i.e. percentage) of the impinging beam is transmitted without change of direction and a portion is reflected through a 90-degree angle. Each portion is reflected back towards the beam splitter by a beam reversing mirror, the return optical path being coincident with the forward path. At the beam splitter recombination of the two portions takes place, with the first now progressing in reflection and the second in transmission towards a common path leading to a light receiving device, which may be a screen or a photoelectric detector.
Now, if the optical path length between the beam splitter and one reversing mirror, which together represent one arm of the interferometer, is made identical with that between the beam splitter and the other reversing mirror, which together represent the other arm of the interferometer, the reflected and transmitted beams will suffer no relative phase changes and consequently will recombine at the beam splitter so as to be indistinguishable--if transmission losses and optical imperfections are notionally assumed to be zero and the beam splitter provides 50% reflection--from the unsplit optical beam.
If, on the other hand, an optical path difference that is significant compared with one half wavelength of the monochromatic light is established between the two arms of the interferometer, such as by moving one of the reversing mirrors towards the beam splitter, interference effects may be expected. The frequency of the resultant sine wave representing the recombined beam will be the same as that of the two constituent sine waves representing the beams prior to their recombination. The amplitude, on the other hand, will be the algebraic sum of the constituent sine waves amplitudes at each successive abscissa point and therefore will vary sinusoidally from a maximum, when the optical path difference is equal to an integral number of wavelengths, and, therefore, the amplitudes of the constituent waves add up (constructive interference), to a minimum, when the optical path difference is equal to an integral number of wavelengths plus one half wavelength and the waves are therefore in phase opposition so that the amplitudes subtract (destructive interference). A series of concentric rings (called interference fringes), representing the maxima and minima of the resultant sine wave, and therefore alternately bright and dark, may be viewed by interposing an ordinary white diffusing screen at the focus of a converging lens interposed in the path of the recombined beam, provided the monochromatic source radiates visible light.
Alternatively and more usefully, the optics of the interferometer may be arranged to project an image of the aperture stop (also called Jacquinot stop) of the interferometer at a photodetector having a circular window for admitting the central interference fringe (i.e. the first ring). This fringe will change from a light to a dark patch as the optical path difference undergoes a change equal to one half wavelength through the movable mirror being displaced between positions corresponding to constructive interference and destructive interference, respectively. The sinusoidal electrical output of the detector can be processed to provide an accurate linear measurement of the mirror displacement and, therefore, of any member suitably mechanically coupled to the mirror, to within a small fraction of one half wavelength. Displacements of exact half wavelengths can, of course, be measured by counting the mean level crossings of the output signal from an appropriate datum. Each crossing counted from the datum represents a change of O.P.D. of exactly half the wavelength of the source, i.e. a displacement of the member of exactly 1/4 wavelength. When a monochromatic source is used the wavelength of which is known precisely, interferometric measurements of length as suggested are perhaps the most sensitive and accurate available to man.
A field of application predicted by Michelson for his interferometer, but only of comparatively recent application, is Fourier Transform spectroscopy (hereinafter FT stands for Fourier Transform). If the movable mirror referred to earlier is actually displaced between a position corresponding to zero O.P.D. and a predetermined limit by mounting the mirror on an accurate scanning assembly following a strictly rectilinear path, the output of the photo-detector will be a sine wave of much lower frequency compared with the monochromatic emission line of the source but constant peak-to-peak amplitude. If it is assumed that the wavelength of the optical input to the detector is, say, 2.5 micrometers and the predetermined limit of the optical path difference is 2 cm then clearly the number of recurrent cycles in the detector output must be 2 cm/0.00025 cm=8000. If the time taken to move the mirror between zero optical path difference and the limit is 1 second, then the frequency of the detector output signal is 8000 Hz. In other words, the original optical wave has been modulated at a frequency of 8000 Hz, well within the audio range. The modulation sine wave, which may be displayed on a CRT, represents the interferogram of the source. If the Fourier Transform of the interferogram is computed, the resulting trace, in the form of a very narrow band, represents the emission line spectrum of the source.
If a broad-band source, e.g. an infrared source, is substituted for the monochromatic source, the output of the detector when the scanning mirror is in motion will no longer be a pure sine wave since the emission spectrum of the source will include waves of different frequencies. Each of the optical sine waves will give rise to two constituent beams and one resultant beam in the manner described earlier and all the resultant beams of different frequencies will be represented in the instantaneous output of the detector, each by its own modulation sine wave of related frequency and amplitude. If the output of the detector is plotted as before, the trace that results represents the emission interferogram of the source.
Now, if a sample not opaque to infrared is placed at the Jacquinot stop, the waves of different frequencies present in the emission spectrum of the source are attenuated to a different extent in a manner that is characteristic of the chemical nature of the sample and the resulting interferogram represents the infrared absorption interferogram of the sample superimposed on the emission interferogram of the source.
By taking the Fourier Transforms of the two interferograms, thus obtaining independently the spectrum of the sample-cum-source and that of the source alone, and then ratioing the first spectrum by the second, the spectrum of the sample is derived. In general the interferogram will consist of a dominant centreband flanked by intermingled waves decrementing more or less symmetrically in amplitude to vanishing values. It is worth observing that there is no point of communality between the various sine waves other than at the position of the scanning mirror corresponding to zero O.P.D. where all waves will undergo constructive interference; and that, of course, is the reason for the presence of the dominant centreband.
It can now be readily appreciated that, whatever the application of the Michelson-type interferometer which necessitates the optical path difference between the two interferometric arms to be changed, a very serious mechanical problem arises.
If mechanical imperfections in the guideways cause the moving mirror to tilt during the scan motion, the effective optical path difference may not be the same for each of several parts of the beam traversing different regions of the beam splitter, with the result that for a given wavelength some parts may be undergoing constructive and some destructive interference. In consequence, the amplitude of the detector signal is spuriously changed compared with the situation where no tilt is present. Servo controls in the form of tilt compensators have been developed but they account for a major portion of the complexity and cost of the entire instrument and can easily get out of adjustment. This is not surprising when it is realized that in a translating-mirror Michelson interferometer the tilt tolerance is typically one or two arc-seconds!
The problem is particularly severe in FT spectrophotometers where a scanning assembly reciprocating along a path of the order of centimeters must be provided. In many experimental and commercial instruments, a rectilinear reciprocating motion is chosen and a great deal of ingenuity has gone into devising means for guiding the assembly so as to confine its motion to a strictly rectilinear path. Linear air bearings and servo controls have been adopted in sophisticated and, therefore, expensive systems.
A practical proposal for a simple rotary scanning assembly which circumvents the major difficulties encountered with rectilinear scanning assemblies and is inherently tilt-compensated to some extent was described by R. S. Sternberg and J. F. James, of the Physical Laboratories of Manchester University, England, in the Journal of Scientific Instruments, Vol. 41, pages 225-226, April 1964, under the title "A new type of Michelson interference spectrometer". In the introduction to their article, the authors stress the drawbacks of scanning arrangements known at the time before discussing their solution. Unfortunately, although their proposal represents an interesting and valuable approach to the problem of lessening mechanical accuracy requirements, it has not been adopted by manufacturers of FT spectrophotometers, probably because it suffers from a serious drawback, now totally eliminated by the present invention.
In modern FT spectrophotometers, the analogue signal generated by the detector is digitized and processed by a microprocessor. It is an important requirement to ensure that the path of the beam reaching the detector does not change with the angular position of the scanning assembly or the optical throughput to the detector will change in a manner which is in no way related to the analysis of the spectrophotometric sample and does in fact vitiate analytical results. It will later be shown with the aid of a drawing, before the disclosure of practical embodiments of the present invention, that such requirement is not met by the prior art proposal, in which the optical output from the scanning assembly suffers a translatory displacement, with the result that, starting from a position of the scanning assembly correspondingly to which the entry pupil of optical converging means before the detector is totally filled, more and more of the rays will miss the pupil altogether as scanning progresses from that position in either rotational direction. The drawback is of course tolerable where the analogue changes in the signal need not be measured accurately, such as when the detector output is merely used for the purpose of counting interference fringes, but is certainly unacceptable in an FT spectrophotometer wherein the spectrum of the sample must be drawn with band amplitude fidelity of a high order.